Nonconvex Quadratic Programming, Semidefinite Relaxations and Randomization Algorithms in Information and Decision Systems

Nonconvex quadratic optimization problems and the methods for their analysis have been on the center stage of information and decision systems for the past 50 years. Although most of these problems are very complex in general, all of them may be relaxed to semidefinite programs. In many cases, this relaxation is tight or it may be bounded. The solution to those programs facilitates the solution to the original nonconvex problem, notably via efficient randomization techniques. Engineering applications of nonconvex quadratic programming and related solution techniques are virtually infinite. Examples extracted from the current literature on information and decision systems are provided. These examples include network optimization problems, linear and nonlinear control problems and important linear algebra problems.

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